I lAD I

MEMORANDUM REPORT ARBRL-MR-03246

(Supersedes IMR No. 738)

HYDRODYNAMIC RAM ATTENUATION

Ki Allister Copland

February 1983

US ARMY ARMAMENT RESEARCH AND DEVELOPMENT COMMANDK BALLISTIC RESEARCH LABORATORY

ABERDEEN PROVING GROUND, MARYLAND

Approved far public release; distribution unlimited.,,, DTIC1-,'-:.Lb•L 1 8 1983

Eý483 02 018 012

Destroy this report when it is no longer needed.Do not return it to the originator.

Additional copies of this report may be obtainedfrom the National Technical Information Service,U. S. Department of Commerce, Springfield, Virginia22161.

The findings in this report are not to be construed asan official Department of the Army position, unlessso designated by other authorized documents.

T'I uet of treade. nome or mufactumr I "noea in this reportdoea not c3)Iati4ot* ino'ivmet of an oonmrcoial produot.

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REPORT DOCUMENTATION PAGE R3AD INMrUCTIONSB&FoRK COMPLZTIG FORM1. REPORT NUMBER "|. •oV ACCESSION NO. R. RECIPIENT'S CATALOG NUMMERMemorandum Report AR.BRL-MR-03246 °" I2-S" 3''

4. TITLIE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

HYDRODYNAMIC RAM ATTENUATION Final

6. PERFORMING ORG. REPORT NUMBER

AUTHOR(e) S. CONTRACT OR GRANT NUMUER(*)

Allister Copland

p. ~_%. -PROGRAM ELEMENT, PROJECT. TASKT..EqOMI qOANIjAT1_0 NAM ,N AgODR,, AREA &A WOKUIUBRUb Army Isaizstic Kesearch LaboratoryATTN: DRDAR- BiLTAberdeen Proving Ground, MD 21005 L162618AH80

1I. CONTROLLING OFFICE NAME AND ADDRESS It. REPORT DATEUS Army Armament Research and Development Command reb_____198US Army Ballistic Research Laboratory (DRDAR-BL) 1S. NUMMEROOF F4GESAberdeen Proving Ground, MD 21005 1814. MONITORING AGENCY NAME A AODRESS(DI diflferet trnm Controlling Ofo16) IS. SECURITY CLASS. (of this report)

Unclassified

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Approved for public release; distribution unlimited.

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IS. SUPPLEMENTARY NOTES

This report supersedes BRL IMR No. 738, dated February 1982.

IS. KEY WORDS (Continue on r,evere side it necessary and identify by block nmbew)Explosafe LVT7Al Amphibious VehicleFoam Fuel FiresHydrodynamic Ram

20. ABSTRACT (Contime on reverse aide II necessary and Identii' byy lock nimnem )Preliminary experiments have been conducted to evaluate the ability of differentinerting agents to attenuate hydrodynamic ram. Standard .50 caliber (12.7 mm)AP bullets and 15/32" (11.9 mm) steel spheres were used to perforate 20 litermetal containers with and without a liquid and Explosafe. Shots were also4nade with .50 caliber (12.7 mm) AP bullets fired at 220 liter drums with andwithout a liquid and safety foam. Initial results indicate that the destructiveeffects of hydrodynamic ram may be enhanced by the additioni of Explosafe to

DO P, AN. 1473 EDITION OF I NOV 6S IS OBSOLETE UNCLASSIFIED

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liquid-containing cells, while the addition of foam may have attenuated theeffects of hydrodynamic ram.

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TABLE OF CONTENTS

Page

I. INTRODUCTION . . . . . . . . . . .5

II. EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . . . .. 7

III. TEST FIRINGS . . . . . . . . . . . . . . . . . . .7

IV. DISCUSSION . .. .. .. .. .. .. .. ... . .. .l

V. CONCLUSIONS . ....................... . . . . . . . . . .12

VI. ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . 12

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 13

TABLE I. 20 Liter Containers ............... 14

TABLE I1. 220 Liter Containers ......... .. . 15

DISTRIBUTION LIST ..................... 17

Acoession ForNTIS GRA&IDTIC TABUnannounced •,Justif icatior•----_j OI

By- -TEDistribution/

Availltbility CodesAv- UI. nid/or

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I. INTRODUCTION

For most of the past docPde~various groups within *he Defense Departmenthave been studying the phenomenon of hydrodynamic ram! 2,3Their efforts havebeen primarily directed toward attenuating its effects on aircraft fuel cellsthrough improvement of fuel cell design methodology, and by the addition ofvarious energy absorbing materials to the insides of fuel cells.

Briefly, hydrodynamic ram is initiated by the impact of a projectile intoa liquid-filled container. 4 Its effects can be divided into three phases:the early shock phase, the later drag phase, and the cavity phase.5 The shockphase results from the energy transferred to the liquid as the projectileperforates the cell and impacts the fluid, creating a strong hemisphericalshock wave centered at the point of impact. This causes an impulsive load onthe inside of the entry wall in the vicinity of the entry hole which may forcethe entry wall to crack and petal In travelling through the liquid, theprojectile loses energy to the fluid. This energy is transformed into kinetic

energy of fluid motion. The projectile is also slowed by viscous drag. As

the fluid is displaced by the moving projectile, a pressure field is generated.This pressure pulse develops gradually as the fluid accelerates, and is of alonger duration, but is less intense than that of the impulsive shock phase. Thecavity phase results from the path left by the moving projectile. This cavityis somewhat conically shaped and contains vapor evaporated from the cavitysurface, and air which can enter the cavity through the entry hole.Oscillation occurs as the fluid seeks to return to its previously undisturbedstate. During this process, additional pressure pulses are generated which aidin the expulsion of fluid from holes in the cell, and contribute to thestructural damage of the fuel cell.

One of 'he major concerns of the users of armored vehicles is theprobability of sustained pool-fires resulting from fuel cell destruction andfuel ignition associated with an impacting projectile. Major research effortshave been concentrated on the development of fire-safe fuels. 6 One of the

1Thomas Bond, "Response of PueZ Celle of the UH-ID Heliooptr to theHydrulic Ram Forces," BRL Memo. Report No. 2289,Apri.! 1973 (AD 910612).

M ic A. Lunds ti o., "Fluid D na'ic AnalZysis of Hydraulic Ram," N. W. C. China

Lake, CA July 1971 (AD 889485L).3Thomas W.Lee and Jerome D.YatteauA, "duic Ram .tn'eet-iation."

University of Denver, Denver Research Inetitute, Denver, Colorado 80210,March 1978.

4Philip F. Fry, "A Review of the AnaZysis of Hydrodynaruic Ram." AFFDL-TR-75-102,August 1976.

5R. E. Ball, "Structural Response of Fluid-Containing Tanks to PenetratingProjecti leas'N.P.S. Monterey, CA. Hydrodcynamic Ram Seminar, AFFDL-TR-77-32.

"W.D.Weatherford, Jr., G.E.Foldor, D.W.Naegeli, E.C.Ocens, B.R.Wright, andF. W. Schackel, "Development of ArEy Fire-Resistant Diesel FuelZ," U.S.ArmySFuels and Lubricats Research Lab.S. W.1I. San Antonio, Teoxw, Dec. 1979

(AD A083610).K"

possible ways fuel may become available to sustain a pool-fire would be dueto leakage resulting from a cell damaged by the forces of hydr'dynamic ram.This memorandum report presents the results of preliminary experiments designedto evaluate zhe effects of various fuel cell filler materials on hydrodynamicram. The two materials examined so far are "Explosafe" and the Type IV bluepolyether reticulated foam. Explosafe is made of an aluminum alloy foil whichis slit and expanded to a hexagonal mesh configuration. Foil mesh batts ofthis material are then cut and shapee for various applications as # protective

mesh in storage containers. Explosafe is manufactured by Vulcan IndustrialPackaging, Ltd., Toronto, Canada. Foam is manufactured by the foam divisionof tho' Scott Paper Company. ThxF material is currently used as an inertingagent in the fuel cells of some of the combat aircrafts of the U. S. Air Force.

Recent research efforts have demonstrated thaý gxplosafe and foam areeffective in attenuating combustion overpressures. I It is believed that byintroducing an energy absorbing medium into fuel cells, that material shouldprovide a shock-absorbing mechanism and act as a retardant for shock wave andpressure pulse generation. Our present objective is to evaluate variousinerting systems for military application in attenuating hydrodynamic ram.Additionally, the Target Effects Branch of the Ballistic Research Laboratoryhas been tasked for FY82 by the Marine Corps Development Center at Qunntico,VA, to evaluate the ballistic response of foam and Explosafe when incorporatedinto liquid-containing fuel cells. As part of a Service Life Extension Program,the Marine Corps is in the process of deciding which inerting system, if any, toinstall inside the fuel cells of the LVT7A1 amphibious vehicles. Not onlyshould we find out if foam or Explosafe can attenuate hydrodynamic ram, weshould also find out if it has any negative effects or no effects at all one wayor the other.

Cells damaged by hydrodynamic ram provide a source of fuel for sustainedpool-fire burning By attenuating hydrodynamiL ram, we decrease the chancesof fuel cell rupture, thus minimizing the availability of fuel for sustainedpool-fires. Sustained pool-fires can result in catastrophic kills forarmored vehicles. Prior to testing fuel cells from the LVT7Al's with andwithout inerting materials and a liquid, a series of field tests was conductedusing 20 and 220 liter metal containers with and without inertingmaterials and liquids. This report details the results of our preliminaryfield testF..

?A. Szego, K.Premji, R.D.AppZeyard, "Evaluation of Explosafe ExplosionSuppression System for Aircraft Fuel Tank Proteotion," Explosafe Division,Vulcan Industrial Packaging Ltd., RexdaZe, Ontario, Canada, July 1980(AD AO 93125).

8A. J.o~ten, "AX Fuel Tank Vu Znen bility Evaluation Report," Air ForceFlight Dynamics Laboratory, AFFDL/PTS Wright-Patterson AFB, OH 45433,July 1974 (AD 922-9166).

6

F-A

II. EXPERIMENTAL PROCEDURE

A series of 12 shots was fired using .SO caliber (12.7 am) standardAP projectiles and 15/32"' (11.9 am) steel spheres aimed at 20 liter fuelcontainers with and without Explosafe, water, and DF 2 diesel fuel. A secondseries of 9 shots was conducted using .50 cal (12.7 ma) standard AP and20 - APIT projectiles aimed at 220 liter drums with and without foam,Explosafe, and water. Two shots were with the 20 mm APIT projectiles,and seven were with the .50 caliber (12.7 m) projectiles. Shots number 1 through12 were with the 20 liter containers (Table 1), and shots number 13 through21 were with the 220 liter containers (Table II). There was onlyone shot conducted with Explosafe and water in a 220 liter drum. Theirnswere conducted at the Peep Site Range of the ERL using rifled Hanni

barrels which are percussion operated and remotely fired. The distancefirings wr odce ttePe ieRneo h R sn ildMnfrom the muzzle to the target was approximately 12 meters. Two standardelectrically conductive velocity screens spaced 60 ca apart were placed 6meter- from the target to make velocity determinations.

The 20 liter containers were purchased frow Explosafe of America,Irvine, CA. They were approximately 38 cm high, and had a diameter ofapproximately 28.5 cm. The tops and bottoms of those cans were used as the entryand exit panels for 11 shots. The projectile travelled 36 cm between entry and exitpanels. The sides of a can were used as the entry and exit panels for 1 shot.All the liquid filled containers were filled to the manufacturer's recommendedfill-level line,leaving approximatily 14% of the volume as ullage space.

The 220 liter drums were standard steel drums with removable tops which werefastened by a retaining metal band. They were approximately 87 cm high and 57cm in diameter. The foam was provided and installed into those drums by theScott Paper Co. For the single shot with Explosafe and water, the Explosafe wasremoved from eleven 20 liter containers and fitted into the 220 liter drim bypersonnel of the Target Effects Branch. All the liquid-conte.i.ning targets withinerting materials contained approximately 200 liters of water. The voided volumerepresented approximately 9% ullage space. The tops ana bottoms of those drumswere used as the entry and exit panels for all the shots. A 16 mum high speedMilliken camera was used for photographic coverage of the events. Coverage ofthree shots is unavailable because of camera malfunction. However, stillphotographs of all the targets are available.

111. TEST FIRINGS

Round #1

A standard .50 caliber AP bullet travelling at approximately 873 m/secwas fired at a container with water but no Explosafe. The tor of the can wasused as the entry panel. The entry hole was approximately 14 nu in diameter andresembled a typical .50 caliber puncture (12.7 mm in diameter). The exit holewas larger, approximately 23 mm long and 15 mm wide. The effects of hydrodynamicram were demonstrated by the entry panel being dislodged from 50% of the perimeterof the panel. The left side of the target was squeezed in, and the exit panel wasbulged out,but not separated at the perimeter.

7

Round #2

This target contained Explosafe and water. The projectile was a standard.SO caliber AP bullet travelling at approximately 907 r/sec. The top andbottom of the can were used as the entry and exit panels. The target wasdestroyed by the bullet. The entry panel was 90% separated from the can withonly a 7.6 cm section of the perimeter remainini attached to the top of thecan. The exit panel was completely removed and torn by the exiting projectile.The side of the can was split open from the top to the bottom. The splitdid not occur at the seam.

Round #3

This shot was a repeat of shot #2 with the projectile travelling at856 a/sec. The entry panel separated from the can over approximately 75% ofthe perimeter. The entry hole exhibited an outward petaling of the surroundingmetal, with a small amnunt of Explospfe coming through the hole. The sidesbulged out in one section, and appj;ared to be squeezed in in two sections.The exit panel was completely removed and torn by the exiting bullet.

Round #4

For this shot, the bottom of the can was used as the entry panel. Thistarget also contained water and Explosafe, and was struck by a standard .SOcaliber AP round travelling at 864 a/sec. The entry penel bulged around theperimeter, but was not separated from the can. The sides were also squeezedin. The exit panel was removed and badly damaged by the exiting projectile.

Round #5

This target contained only Explosafe and air, no liquid. The impacting.SO caliber bullet was travelling at 890 i/sec. The only damage to thepanels was entry and exit holes approximately 2 ca in diameter. There wasno other damage to the target.

Round #6

This target had air only and was without Explosafe or any liquid. ThewO caliber projectile was travelling at 886 M/sec. Again, the only damagewas entry and exit holes approximately I.S cm in diameter. There was noother damage to the target.

Round #7

This target had Explosafe, but was without any liquid. The .SO caliberbullet was travelling at 866 m/sec. For this shot, the entry panel impactpoint was in an area where the handle of the can was spot welded to the topof the can in order to induce tumbling of the round. As a result, the entryand exit panels had larger holes than those of shots #S and #6. Theymeasured approximately 5 cm in diameter. There was uno other damage to thetarget.

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Round #8

"This shot was made with the sides of the can bein used as the entry andexit panels. The can contained water and EXplosafe. The impacting .TOcaliber projectile was travelling at 890 a/sec. The entry side exhibited aneat perforation (about I.$ cm in diameter). There was a large exit holewith tremendous petaling and splitting of the can along the seam. There wasalso a large conical cavity made into the Explosafe as a result of thecavitation phase behind the round. The left side of the target (top of can)was about 80% separated from the perimeter, and the right side (bottom of thecan) bulged around the perimeter.

Round #9

This was the first of three shots using a 15/32" (11.9 am) steel sphere

as the impacting projectile. For this target, the can contained water but noExplosafe. The impacting projectile was travelling at 1044 in/sec. Therewas a neat entry panel perforation with the panel bulging around the perimeter.The exit hole was also a neat perforation with that panel bulging andseparated from about 10% of the perimeter. Both entry and exit holes wereabout 1.2 cm in diameter. The sides were also squeezed in.

Rounds #10 and #11

The targets for these tests were Explosafe filled cans with water. Theprojectiles were 15/32" (11.9 m) steel spheres travelling at 1022 M/sec and1045 a/sec,respectively. Both entry panels were neatly perforated by thespheres. The panels also bulged at the perimeters. Both cans were split openalong their seams. The exit panels were also bulging around their perimeters,but there were no panel separations. In both cases, the entry and exit holeswere approximately 1.2 cm in diameter. There was no other damage to thetargets.

Round # 12

For this test, DF2 diesel fuel was used as the liquid in an Explosafefilled can. A .50 caliber AP projectile travelling at 904 m/sec was used forthis shot. The entry panel was neatly perforated (about S.5 cm in diameter)and bulging occurred at the perimeter of the can. There were two tears alongthe sides of the can; one extended from the top to the bottom, while the otherwas only about 12.7 cm long. The exit panel was completely destroyed andremoved. Some of the Explosafe material was also pushed out from the can.

Round #13

This was the first shot using the 220 liter drums. This target containedwater only, and was hit with a 20 =e projectile travelling at appr..imately1101 .n/sec. The entry panel or top of drum was completely removed as a result

of the projectile's impact. The exit panel was separated over approximately

98% of the perimeter. The entry hole was about 2 cm in diameter, while theexit hole was a large tear about 14 cm long and 14 cm wide with severe ,-taling.The sides were badly squeezed in.

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Round 914

For this shot, the drum contained foam and water, and was perforatedwith a 20 = projectile travelling at 106S r/sec. The entry hole was aneat puncture with the entry panel completely separated. The exit panelwas badly bulged and separated about 7.6 cm from the perimeter. The sidesof the target were partly squeezed in.

Round #15

Fer ".his shot, the 220 liter drum contained water only, and wasperforated by a .S0 caliber projectile travelling at 889 a/sec. The entrypanel was completely separated, and the sides were badly squeezed. The exitpanel bulged around the perimeter, and had an exit hole about 5.3 cm longand 2 cm wide. The size of the exit hole is representative of one created bya side-on impacting projectile.

Round #16

This target contained foam and water. The impacting .50 caliber projectilewas travelling approximately 910 r/sec. The entry panel bulged around theperimeter, but was not separated. The sides were slightly squeezed in. Theexit panel bulged in the vicinity of the exit hole which was about 4.6 cm longand 1.5 cm wide. This hole was also caused by a side-on impact.

Round #17

This target contained water only, and was impacted with a .50 caliberbullet travelling at 859 m/sec. The entry panel of this target wascompletely separated while the sides were badly squeezed in. The exit panelbulged around the perimeter. The exit puncture resulting frmm a side-onimpact was approximately 5.5 cm long and 2 cm wide.

Round #18

This target contained water and foam. The impacting .SO caliber bullettravelled at 867 m/sec. The entry panel bulged around the perimeter and thesides were squeezed in. The exit panel also bulged around its perimeter.

Round #19

For this shot, the 220 liter drum contained air only. The entry and

exit panels experienced neat entry and exit holes. There was no other damageto this target. The .50 caliber projectile impacted the target at approxi-mately 901 M/sec.

Round #20

This target containad foam and soapy water. It is believed that byusing soapy water, we promoted better wetting between the liquid and foam,thus minimizing the amount of air trapped within the cavities of the foaminside the target. Because of the compressibility of the air, it is possibleto experience an additional attenuating effect which may increase the action

10K . . . . . . - -.|- - -- z . .~

of the foam. The .SO caliber round travelled et approximately 917 a/sec." The entry panel of this target bulged around the perimeter, Ahile the: sides

were squeezed in. The exit panel also bulged around the perimeter. Theresults of this shot were similar to those containing plain water and foam.

Round #21

This was the only shot in which Explosafe was installed inside a 220 litercontainer. Because this material is normally installed by the manufacturerin 20 liter containers, we removed the Explosafe from eleven cans, and installedit in the 220 liter drum. In addition to the Explosafe, the target containedwater. The impacting .SO caliber projectile travelled at approximately 905a/sec. The entry panel bulged and separated, while the sides were squeezed in,The exit panel bulged around the perimeter.

IV. DISCUSSION

The effects of hydrodynamic rem were very evident after each shot witha liquid containing target. The destructive effects appeared to have beenenhanced by the presence of Explosafe in the 20 liter containers, especiallyin the case of the .50 caliber bullets. The geometric configuration of thesepiojectiles is significant; in travelling through the liquid, they alwaystumble. Additionally, they appeared to have become entangled with theExplosafe material. As a result, these projectiles carried portions of thismaterial with them to the exit panels. This piston-like action may havecreated an extra loading on these panels, thereby increasing the destructive

effects of hydrodynamic ram.

Lesser damage was caused by the 15/32" (11.9 am) spheres. In additionto having smaller masses, their shape permitted them to travel to the exitpanels, experiencing less interaction with the Explosafe. A significantportion of the kinetic energy appeared to have been expended radially into

developing fluid motion. In the tests using spheres against targets withExplosafe and a liquid, more damage was done to the sides of those targetsthan to either of the panels.

In the series using 220 liter drums, lesser "amage occurred when thetargets contained foam in comparison to those with.rut foam. The differencesin structural damage indicate that the foam acted 's an energy absorbing medium.

In all the shots made with foam, water, and .50 caliber projectiles,none of the entry panels separated from the targets. The exit panelsexperienced less bulging, and the exit holes were smaller when compared tothe targets shot with water only. The sides were also less damaged.

There were only two shots made with the 20 mm projectiles. After thoseshots, we decided that the impacting energy associated with each round wastoo much of an overmatch for the target for us to discern any significantdifferences in ballistic response due to target set-up. The entry panelsseparated from both targets. For the target containing foam and water, theexit panel experienced less separation from its perimeter than the target

* 11

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with water only.

One shot was made with Explosafe and water in a 220 liter drum. Forthat shot, there is no physical evidence of any increase or decrease indamage to the target when compared to the targets that contained water only.The entry panel separated. The exit panel bulged, and the sides were badlysqueezed in. The batts of Explosafe used in this target had been removedfrom 20 liter containers. It would have been ideal to have had one largecylindrically shaped batt for this target; however, commiercial containerswith Explosafe larger than a 20 liter capacity are not easily available.

We are presently involved in testing fuel cells supplied by themanufacturer of the LVT7A1 amphibious landing vehicle. These cells willcontain different inerting systems. Upon completion of our testing, adefinitive judgment and recommendations will be made after evaluating theattenuating properties, in any, of foam or Explosafe.

V. CONCLUSIONS

Subject to the targets and threats used, our tests indicate the following:

1. The destructive effects of hydrodynamic ram were enhanced byExplosafe in the 20 liter containers.

2. Foam acted as a retardant for pressure pulse generation in the220 liter containers, thereby reducing the effects bf'hydrodynamic ram.

3. Explosafe demonstrated no positive or negative effects in theone 220 liter target used.

VI. ACKNOWLEDGMENTS

The author wishes to thank Mr. Bernard Izdebski and Mr. Robert McGillfor carrying out the firing program at the Peep Site Range of the BRL.

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REFERENCES

1. Thomas Bond, "Response of Fuel Cells of the UH-1D Helicopter to theHydraulic Ram Forces," BRL Memo. Report No. 2289, April 1973 (AD 910612).

2. Eric A. Lundstrom, "Fluid Dynamic Analysis of Hydraulic Ram," N.W.C. ChinaLake, CA, July 1971 (AD 889485L).

3. Thomas W. Lee and Jerome D. Yatteau, "Hydraulic Ram Investigation,"

University of Denver, Denver Research Institute, Denver, Colorado 80210,March 1978.

4. Philip F. Fry, "A Review of the Analysis of Hydrodynamic Ram," AFFDL-TR-75-102,

August 1976.

5. R. E. Ball, "Structural Response of Fluid-Containing Tanks to PenetratingProjectiles," N.P.S. Monterey, CA. Hydrodynamic Ram Seminar, AFFDL-TR-77-32.

6. W. D. Weatherford, Jr., G. E. Foldor, D. W. Naegeli, E. C. Owens, B. R. Wright,and F. W. Schackel, "Development of Army Fire-Resistant Diesel Fuel," U.S. ArmyFuels and Lubricants Research Lab. S.W.I. San Antonio, Texas, Dec. 1979

(AD A083610).

7. A. Szego, K. Premji, R. D. Appleyard, "Evaluation of Explosafe ExplosionSuppression System for Aircraft Fuel Tank Protection," Explosafe Division,Vulcan Industrial Packaging Ltd., Rexdale, Ontario, Canada, July 1980(AD AO 93125).

8. A. J. Holten, "AX Fuel Tank Vulnerability Evaluation Report," Air ForceFlight Dynamics Laboratory, AFFDL/PTS Wright-Patterson AFB, OH 45433,

July 1974 (AD 922-9166).

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5. General Comments (Indicate what you think should be changed tomake this report and future reports of this type more responsiveto your needs, more usable, improve readability, etc.)______

6. If you would like to be contacted by the personnel who preparedthis report to raise specific questions or discuss the topic,please fill in the following information.

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